Question

How many solutions does this system have?

Answer 1

Answer:

The correct option is d.

Step-by-step explanation:

The given equations are

$x-2y=2$                 .... (1)

$y=-2x+5$               .... (2)

In equation 2, multiply both sides by 2.

$2y=-4x+10$               .... (3)

Now add equation (1) and (3).

$x-2y+2y=2+(-4x+10)$

$x=2-4x+10$

$x+4x=12$

$5x=12$

Divide both sides by 5.

$x=\frac{12}{5}=2.4$

Put this value in equation (2).

$y=-2(2.4)+5$

$y=-4.8+5$

$y=0.2$

Therefore the solution of the system of equation is (2.4,0.2) and the system has only one solution. Option d is correct.

Answer 2

X-2y=2
y=-2x+5
A. Infinitely many solutions
B. No Solutions
C. Two Solutions
D. One Solution*****